Running the cards more than once is a way to decrease the variance in a hand by chopping the pot into multiple, smaller pots. If you run the cards twice there are two pots, three times three pots and so on and so forth.
No matter what anyone tells you running the board multiple times does not change the odds of the hand. There is no strategy behind it and it makes no difference what you hold. Running it more than once only decreases the variance. The more times that you run it the closer the result will come to the actual equity in the hand. Running cards multiple times came about from trying to keep games from breaking and keeping people in action. If a player went bust and there were not enough people to fill the table the game would sometimes die.
Now, more and more casinos are allowing players to run it more than once and some players are trying to take advantage of the situation. Players commonly ask when deciding whether or not to make big calls all-in if the other player in the hand will run it more than once. This is an issue especially when you are trying to maximize your fold equity with a draw. Why would you want your opponent to know that you will run it more than once and not instill the fear that he could lose all of his chips? It also works the other way around when players try to push you around with their draws. If they know that you will run it more than once they are more likely to make an aggressive action because if they get called there is less of a chance that they will lose all of their chips.
A second and probably more important reason that I don’t like to run the cards is because I feel like I have better emotional control than most other players. If I lose a big pot I am way less likely to tilt compared to my opponents. As the skill level of players start to increase you’ll find that a lot of money is won and lost when certain players tilt. You want to give those players the opportunity to lose their cool. One of the best ways to do this is to break them—not give them an opportunity to win back some of the pot.